Probability

A problem is given to three students \(A,B\) and \(C\), whose probabilities of solving the problem independently are \(\frac{1}{2},\frac{3}{4}\) and \(p\) respectively. If the probability that the problem can be solved is \(\frac{29}{32}\), then what is the value of \(p\)?

If \(A\) and \(B\) are events such that \(\mathrm{P}(\mathrm{A}/\mathrm{B})=\mathrm{P}(\mathrm{B}/\mathrm{A})\neq 0\), then :

If \(E\) and \(F\) are two events such that \(P(E)>0\) and \(P(F) \neq 1\), then \(P(\overset{¯}{\mathrm{E}}/\overset{¯}{\mathrm{F}})\) is

Let \(E\) be an event of a sample space \(S\) of an experiment, then \(P(S \mid E)=\)

If A and B are events such that \(\mathrm{P}(\mathrm{A}/\mathrm{B})=\mathrm{P}(\mathrm{B}/\mathrm{A})\neq 0\), then :

If \(E\) and \(F\) are two events such that \(P(E)>0\) and \(P(F) \neq 1\), then \(P(\overset{¯}{\mathrm{E}}/\overset{¯}{\mathrm{F}})\) is

If \(\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)\), then which of the following statements is true?

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random are found to be 1 red and 1 black. If the probability that both balls come from Bag A is \(\frac{6}{11},\) then n is equal to_______.

[JEE Main 2022, 24 Jun (Shift 1)]

Let \(E\) be an event of a sample space \(S\) of an experiment, then \(P(S \mid E)=\)

If \(\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)\), then which of the following statements is true?

If \(P(E)=0.05\), then the probability of 'Not E ' will be :

The probability of obtaining an odd prime number on each die, when a pair of dice is rolled, is :

The probability of obtaining an even prime number on each die, when a pair of dice is rolled, is -

In a throw of a die, determine the probability of getting a number more than 4:

If \(\mathrm{P}(\mathrm{A})=\frac{7}{13},\mathrm{P}(\mathrm{B})=\frac{9}{13}\) and \(\mathrm{P}(\mathrm{A}\cap \mathrm{B})=\frac{4}{13}\),

then the value of \(\mathrm{P}(\mathrm{A}/\mathrm{B})\) is -

If \(P(A)=0.5,P(B)=0\), then \(P(A∣B)\) is

If a coin is tossed three times, where E : head on third toss; F :

heads on first two tosses, then the value of \(\mathrm{P}(\mathrm{E}/\mathrm{F})\) is -

If a pair of dice is thrown, then the probability of getting

an even prime number on each die is -

Let \(\Omega\) be the sample space and \(A \subseteq \Omega\) be an event. Given below are two statements:
\(({S}_{1}):\) If \(P(A)=0\), then \(A=\phi\)
\(({S}_{2}):\) If \(P(A)=1\), then \(A=\Omega\)
Then